Just a quick comment on your car rental plans - it's usually considerably more expensive to pick up a car at an airport than at a city location. Even though it sounds like you're on a pretty tight schedule and starting out with a train trip might eat up too much precious time, I'd look into something like starting with a train to Chatres or one of your other destinations, picking up a car there, driving to the other places and then back to Paris to drop off the car.

Others in the group have, I'm sure, much more experience than me and might offer some advice.

Regards, Al Sonoma, CA, USA